Multiple choice

A solid cylinder of height 9 meter has its curved surface area equal to one third of the total surface area. What is the radius of the base?

  1. 9 meter

  2. 18 meter

  3. 27 meter

  4. 30 meter
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

CSA = 2πrh, TSA = 2πr(r+h). Given: CSA = TSA/3 → 2πrh = 2πr(r+h)/3 → 6πrh = 2πr(r+h) → 6h = 2(r+h) → 6h = 2r + 2h → 4h = 2r → r = 2h = 2(9) = 18 m. Check: CSA = 2π(18)(9) = 324π, TSA = 2π(18)(27) = 972π, CSA/TSA = 324/972 = 1/3 ✓. Option A (9 m), C (27 m), and D (30 m) don't satisfy the condition.

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